Shear-Induced Heterogeneity in Associating Polymer Gels: Role of Network Structure and Dilatancy

We study associating polymer gels under steady shear using Brownian dynamics simulation to explore the interplay between the network structure, dynamics, and rheology. For a wide range of flow rates, we observe the formation of shear bands with a pronounced difference in shear rate, concentration, and structure. A striking increase in the polymer pressure in the gradient direction with shear, along with the inherently large compressibility of the gels, is shown to be a crucial factor in destabilizing homogeneous flow through shear-gradient concentration coupling. We find that shear has only a modest influence on the degree of association, but induces marked spatial heterogeneity in the network connectivity. We attribute the increase in the polymer pressure (and polymer mobility) to this structural reorganization.

Figure 1

Effect of $T^{*}$ on (a) the weight-averaged cluster size distribution; (b) $\tau$, $D$, ${\sigma }_{xz,\gamma }$, and $\mathrm{\Pi }$. The subscript $R$ indicates properties of our Rouse system with $D_R=6\times {10}^{-3}$ and ${\mathrm{\Pi }}_R=8.9nkT$. $G_0$ is the gel shear modulus at $T^{*}=0.174$.

Figure 2

(a) Constitutive curves (obtained with a combination of sweep and startup protocols) for the gel at $T^{*}=0.174$ and for the Rouse solution. The insets display the AP velocity and density profiles at various shear rates. (b) Profiles for concentration $\rho$, velocity $u$ ($U_{\max }=\dot{\gamma }{L}_z$), bridging density $n_B$, and cluster functionality $f$. The subscript “eq” denotes equilibrium properties. (c) Snapshot of banded flow (only stickers are shown for clarity).

Figure 3

(a) $({\mathrm{\Pi }}_{zz}-{\mathrm{\Pi }}_{\mathrm{eq}})/{\mathrm{\Pi }}_{\mathrm{eq}}$ as a function of $\dot{\gamma }$ and $T^{*}$. (b) Influence of $\dot{\gamma }$ on the cluster size distribution of the AP gel ($T^{*}=0.174$). (c) Weight-averaged DRA size distribution (with the chains binned into groups of 20) excluding clusters with $Z_c<4$. (d) Diffusivity in the gradient $D_{zz}$ and vorticity $D_{yy}$ directions in the regime of homogeneous flow. (e) Breakup of a single space-spanning DRA at equilibrium (left) to several smaller DRAs (indicated by different colors) during steady shear at $\dot{\gamma }={10}^{-2}$ (right). Stickers not belonging to a DRA are shown in grey.